On the numerical integration of ordinary differential equations of the first order

Abstract

The difference methods for the numerical integration of ordinary differential equations of the first order are discussed by using operator calculus and symbolic expansions. A new straightforward central difference method is developed, which is based on a formula closely associated with Simpson’s rule. The main features of the method are that, for each step of integration, the largest unknown term is determined by an algebraic equation and that the remaining difference correction is extremely small. The method can directly be applied even to systems of the first order with one-point boundary conditions. A numerical example is given.